\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  -7.0 & -7.00 x_{1} & -7.00 x_{2} & + 10.00 x_{3} & +  5.00 x_{4} & -8.00 x_{5} & +  4.00 x_{6} & +  7.00 x_{7} & -10.00 x_{8}\\
 x_{10}   &  28.0 & -5.00 x_{1} & -2.00 x_{2} & -3.00 x_{3} & + 10.00 x_{4} & +  5.00 x_{5} & +  3.00 x_{6} & -10.00 x_{7} & -9.00 x_{8}\\
 x_{11}   &  35.0 & -6.00 x_{1} & -6.00 x_{2} & -8.00 x_{3} & -1.00 x_{4} & +  5.00 x_{5} & +  1.00 x_{6} & -9.00 x_{7} & +  6.00 x_{8}\\
 x_{12}   &  -13.0  &   & -3.00 x_{2} & +  7.00 x_{3} & +  7.00 x_{4} & +  5.00 x_{5} & +  5.00 x_{6} & -10.00 x_{7} & -5.00 x_{8}\\
 x_{13}   &  -11.0 & +  5.00 x_{1} & -2.00 x_{2} & +  2.00 x_{3} & +  6.00 x_{4} & -9.00 x_{5} & +  8.00 x_{6} & +  5.00 x_{7} & -3.00 x_{8}\\
\hline
z    &  0.0 & -4.00 x_{1} & -4.00 x_{2} & +  4.00 x_{3} & -5.00 x_{4} & -4.00 x_{5} & +  3.00 x_{6} & -3.00 x_{7} & -3.00 x_{8}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{8}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,13$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  7.00 y_{9} & +  5.00 y_{10} & +  6.00 y_{11} &   & -5.00 y_{13}\\
 y_{2}   &  1.0 & +  7.00 y_{9} & +  2.00 y_{10} & +  6.00 y_{11} & +  3.00 y_{12} & +  2.00 y_{13}\\
 y_{3}   &  1.0 & -10.00 y_{9} & +  3.00 y_{10} & +  8.00 y_{11} & -7.00 y_{12} & -2.00 y_{13}\\
 y_{4}   &  1.0 & -5.00 y_{9} & -10.00 y_{10} & +  1.00 y_{11} & -7.00 y_{12} & -6.00 y_{13}\\
 y_{5}   &  1.0 & +  8.00 y_{9} & -5.00 y_{10} & -5.00 y_{11} & -5.00 y_{12} & +  9.00 y_{13}\\
 y_{6}   &  1.0 & -4.00 y_{9} & -3.00 y_{10} & -1.00 y_{11} & -5.00 y_{12} & -8.00 y_{13}\\
 y_{7}   &  1.0 & -7.00 y_{9} & + 10.00 y_{10} & +  9.00 y_{11} & + 10.00 y_{12} & -5.00 y_{13}\\
 y_{8}   &  1.0 & + 10.00 y_{9} & +  9.00 y_{10} & -6.00 y_{11} & +  5.00 y_{12} & +  3.00 y_{13}\\
\hline
z    &  -0 & +  7.00 y_{9} & -28.00 y_{10} & -35.00 y_{11} & + 13.00 y_{12} & + 11.00 y_{13}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 4 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  7.00 y_{9} & +  5.00 y_{10} & +  6.00 y_{11} &   & -5.00 y_{13}\\
 y_{2}   &  1.42857142857 & +  4.86 y_{9} & -2.29 y_{10} & +  6.43 y_{11} & -0.43 y_{4} & -0.57 y_{13}\\
 y_{3}   &  6.93889390391e-17 & -5.00 y_{9} & + 13.00 y_{10} & +  7.00 y_{11} & +  1.00 y_{4} & +  4.00 y_{13}\\
 y_{12}   &  0.142857142857 & -0.71 y_{9} & -1.43 y_{10} & +  0.14 y_{11} & -0.14 y_{4} & -0.86 y_{13}\\
 y_{5}   &  0.285714285714 & + 11.57 y_{9} & +  2.14 y_{10} & -5.71 y_{11} & +  0.71 y_{4} & + 13.29 y_{13}\\
 y_{6}   &  0.285714285714 & -0.43 y_{9} & +  4.14 y_{10} & -1.71 y_{11} & +  0.71 y_{4} & -3.71 y_{13}\\
 y_{7}   &  2.42857142857 & -14.14 y_{9} & -4.29 y_{10} & + 10.43 y_{11} & -1.43 y_{4} & -13.57 y_{13}\\
 y_{8}   &  1.71428571429 & +  6.43 y_{9} & +  1.86 y_{10} & -5.29 y_{11} & -0.71 y_{4} & -1.29 y_{13}\\
\hline
z    &  1.85714285714 & -2.29 y_{9} & -46.57 y_{10} & -33.14 y_{11} & -1.86 y_{4} & -0.14 y_{13}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  2.28571428571 & -7.00 x_{1} & -4.86 x_{2} & +  5.00 x_{3} & +  0.71 x_{12} & -11.57 x_{5} & +  0.43 x_{6} & + 14.14 x_{7} & -6.43 x_{8}\\
 x_{10}   &  46.5714285714 & -5.00 x_{1} & +  2.29 x_{2} & -13.00 x_{3} & +  1.43 x_{12} & -2.14 x_{5} & -4.14 x_{6} & +  4.29 x_{7} & -1.86 x_{8}\\
 x_{11}   &  33.1428571429 & -6.00 x_{1} & -6.43 x_{2} & -7.00 x_{3} & -0.14 x_{12} & +  5.71 x_{5} & +  1.71 x_{6} & -10.43 x_{7} & +  5.29 x_{8}\\
 x_{4}   &  1.85714285714  &   & +  0.43 x_{2} & -1.00 x_{3} & +  0.14 x_{12} & -0.71 x_{5} & -0.71 x_{6} & +  1.43 x_{7} & +  0.71 x_{8}\\
 x_{13}   &  0.142857142857 & +  5.00 x_{1} & +  0.57 x_{2} & -4.00 x_{3} & +  0.86 x_{12} & -13.29 x_{5} & +  3.71 x_{6} & + 13.57 x_{7} & +  1.29 x_{8}\\
\hline
z    &  -1.85714285714 & -1.00 x_{1} & -1.43 x_{2} & -0.00 x_{3} & -0.14 x_{12} & -0.29 x_{5} & -0.29 x_{6} & -2.43 x_{7} & -1.71 x_{8}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  2.28571428571 & -7.00 x_{1} & -4.86 x_{2} & +  5.00 x_{3} & +  0.71 x_{12} & -11.57 x_{5} & +  0.43 x_{6} & + 14.14 x_{7} & -6.43 x_{8}\\
 x_{10}   &  46.5714285714 & -5.00 x_{1} & +  2.29 x_{2} & -13.00 x_{3} & +  1.43 x_{12} & -2.14 x_{5} & -4.14 x_{6} & +  4.29 x_{7} & -1.86 x_{8}\\
 x_{11}   &  33.1428571429 & -6.00 x_{1} & -6.43 x_{2} & -7.00 x_{3} & -0.14 x_{12} & +  5.71 x_{5} & +  1.71 x_{6} & -10.43 x_{7} & +  5.29 x_{8}\\
 x_{4}   &  1.85714285714  &   & +  0.43 x_{2} & -1.00 x_{3} & +  0.14 x_{12} & -0.71 x_{5} & -0.71 x_{6} & +  1.43 x_{7} & +  0.71 x_{8}\\
 x_{13}   &  0.142857142857 & +  5.00 x_{1} & +  0.57 x_{2} & -4.00 x_{3} & +  0.86 x_{12} & -13.29 x_{5} & +  3.71 x_{6} & + 13.57 x_{7} & +  1.29 x_{8}\\
\hline
z    &  -9.28571428571 & -4.00 x_{1} & -6.14 x_{2} & +  9.00 x_{3} & -0.71 x_{12} & -0.43 x_{5} & +  6.57 x_{6} & -10.14 x_{7} & -6.57 x_{8}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  2.28571428571 & -7.00 x_{1} & -4.86 x_{2} & +  5.00 x_{3} & +  0.71 x_{12} & -11.57 x_{5} & +  0.43 x_{6} & + 14.14 x_{7} & -6.43 x_{8}\\
 x_{10}   &  46.5714285714 & -5.00 x_{1} & +  2.29 x_{2} & -13.00 x_{3} & +  1.43 x_{12} & -2.14 x_{5} & -4.14 x_{6} & +  4.29 x_{7} & -1.86 x_{8}\\
 x_{11}   &  33.1428571429 & -6.00 x_{1} & -6.43 x_{2} & -7.00 x_{3} & -0.14 x_{12} & +  5.71 x_{5} & +  1.71 x_{6} & -10.43 x_{7} & +  5.29 x_{8}\\
 x_{4}   &  1.85714285714  &   & +  0.43 x_{2} & -1.00 x_{3} & +  0.14 x_{12} & -0.71 x_{5} & -0.71 x_{6} & +  1.43 x_{7} & +  0.71 x_{8}\\
 x_{13}   &  0.142857142857 & +  5.00 x_{1} & +  0.57 x_{2} & -4.00 x_{3} & +  0.86 x_{12} & -13.29 x_{5} & +  3.71 x_{6} & + 13.57 x_{7} & +  1.29 x_{8}\\
\hline
z    &  -9.28571428571 & -4.00 x_{1} & -6.14 x_{2} & +  9.00 x_{3} & -0.71 x_{12} & -0.43 x_{5} & +  6.57 x_{6} & -10.14 x_{7} & -6.57 x_{8}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{13} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  2.46428571429 & -0.75 x_{1} & -4.14 x_{2} & -1.25 x_{13} & +  1.79 x_{12} & -28.18 x_{5} & +  5.07 x_{6} & + 31.11 x_{7} & -4.82 x_{8}\\
 x_{10}   &  46.1071428571 & -21.25 x_{1} & +  0.43 x_{2} & +  3.25 x_{13} & -1.36 x_{12} & + 41.04 x_{5} & -16.21 x_{6} & -39.82 x_{7} & -6.04 x_{8}\\
 x_{11}   &  32.8928571429 & -14.75 x_{1} & -7.43 x_{2} & +  1.75 x_{13} & -1.64 x_{12} & + 28.96 x_{5} & -4.79 x_{6} & -34.18 x_{7} & +  3.04 x_{8}\\
 x_{4}   &  1.82142857143 & -1.25 x_{1} & +  0.29 x_{2} & +  0.25 x_{13} & -0.07 x_{12} & +  2.61 x_{5} & -1.64 x_{6} & -1.96 x_{7} & +  0.39 x_{8}\\
 x_{3}   &  0.0357142857143 & +  1.25 x_{1} & +  0.14 x_{2} & -0.25 x_{13} & +  0.21 x_{12} & -3.32 x_{5} & +  0.93 x_{6} & +  3.39 x_{7} & +  0.32 x_{8}\\
\hline
z    &  -8.96428571429 & +  7.25 x_{1} & -4.86 x_{2} & -2.25 x_{13} & +  1.21 x_{12} & -30.32 x_{5} & + 14.93 x_{6} & + 20.39 x_{7} & -3.68 x_{8}\\
\end{array}\]


 $ x_{1} $ enters and $ x_{4} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  1.37142857143 & +  0.60 x_{4} & -4.31 x_{2} & -1.40 x_{13} & +  1.83 x_{12} & -29.74 x_{5} & +  6.06 x_{6} & + 32.29 x_{7} & -5.06 x_{8}\\
 x_{10}   &  15.1428571429 & + 17.00 x_{4} & -4.43 x_{2} & -1.00 x_{13} & -0.14 x_{12} & -3.29 x_{5} & + 11.71 x_{6} & -6.43 x_{7} & -12.71 x_{8}\\
 x_{11}   &  11.4 & + 11.80 x_{4} & -10.80 x_{2} & -1.20 x_{13} & -0.80 x_{12} & -1.80 x_{5} & + 14.60 x_{6} & -11.00 x_{7} & -1.60 x_{8}\\
 x_{1}   &  1.45714285714 & -0.80 x_{4} & +  0.23 x_{2} & +  0.20 x_{13} & -0.06 x_{12} & +  2.09 x_{5} & -1.31 x_{6} & -1.57 x_{7} & +  0.31 x_{8}\\
 x_{3}   &  1.85714285714 & -1.00 x_{4} & +  0.43 x_{2} &   & +  0.14 x_{12} & -0.71 x_{5} & -0.71 x_{6} & +  1.43 x_{7} & +  0.71 x_{8}\\
\hline
z    &  1.6 & -5.80 x_{4} & -3.20 x_{2} & -0.80 x_{13} & +  0.80 x_{12} & -15.20 x_{5} & +  5.40 x_{6} & +  9.00 x_{7} & -1.40 x_{8}\\
\end{array}\]


 $ x_{6} $ enters and $ x_{1} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  8.08695652174 & -3.09 x_{4} & -3.26 x_{2} & -0.48 x_{13} & +  1.57 x_{12} & -20.13 x_{5} & -4.61 x_{1} & + 25.04 x_{7} & -3.61 x_{8}\\
 x_{10}   &  28.1304347826 & +  9.87 x_{4} & -2.39 x_{2} & +  0.78 x_{13} & -0.65 x_{12} & + 15.30 x_{5} & -8.91 x_{1} & -20.43 x_{7} & -9.91 x_{8}\\
 x_{11}   &  27.5869565217 & +  2.91 x_{4} & -8.26 x_{2} & +  1.02 x_{13} & -1.43 x_{12} & + 21.37 x_{5} & -11.11 x_{1} & -28.46 x_{7} & +  1.89 x_{8}\\
 x_{6}   &  1.10869565217 & -0.61 x_{4} & +  0.17 x_{2} & +  0.15 x_{13} & -0.04 x_{12} & +  1.59 x_{5} & -0.76 x_{1} & -1.20 x_{7} & +  0.24 x_{8}\\
 x_{3}   &  1.0652173913 & -0.57 x_{4} & +  0.30 x_{2} & -0.11 x_{13} & +  0.17 x_{12} & -1.85 x_{5} & +  0.54 x_{1} & +  2.28 x_{7} & +  0.54 x_{8}\\
\hline
z    &  7.58695652174 & -9.09 x_{4} & -2.26 x_{2} & +  0.02 x_{13} & +  0.57 x_{12} & -6.63 x_{5} & -4.11 x_{1} & +  2.54 x_{7} & -0.11 x_{8}\\
\end{array}\]


 $ x_{7} $ enters and $ x_{6} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  31.3090909091 & -15.84 x_{4} & +  0.38 x_{2} & +  2.71 x_{13} & +  0.65 x_{12} & + 13.11 x_{5} & -20.55 x_{1} & -20.95 x_{6} & +  1.40 x_{8}\\
 x_{10}   &  9.18181818182 & + 20.27 x_{4} & -5.36 x_{2} & -1.82 x_{13} & +  0.09 x_{12} & -11.82 x_{5} & +  4.09 x_{1} & + 17.09 x_{6} & -14.00 x_{8}\\
 x_{11}   &  1.2 & + 17.40 x_{4} & -12.40 x_{2} & -2.60 x_{13} & -0.40 x_{12} & -16.40 x_{5} & +  7.00 x_{1} & + 23.80 x_{6} & -3.80 x_{8}\\
 x_{7}   &  0.927272727273 & -0.51 x_{4} & +  0.15 x_{2} & +  0.13 x_{13} & -0.04 x_{12} & +  1.33 x_{5} & -0.64 x_{1} & -0.84 x_{6} & +  0.20 x_{8}\\
 x_{3}   &  3.18181818182 & -1.73 x_{4} & +  0.64 x_{2} & +  0.18 x_{13} & +  0.09 x_{12} & +  1.18 x_{5} & -0.91 x_{1} & -1.91 x_{6} & +  1.00 x_{8}\\
\hline
z    &  9.94545454545 & -10.38 x_{4} & -1.89 x_{2} & +  0.35 x_{13} & +  0.47 x_{12} & -3.25 x_{5} & -5.73 x_{1} & -2.13 x_{6} & +  0.40 x_{8}\\
\end{array}\]


 $ x_{8} $ enters and $ x_{11} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  31.7511961722 & -9.43 x_{4} & -4.19 x_{2} & +  1.75 x_{13} & +  0.51 x_{12} & +  7.07 x_{5} & -17.97 x_{1} & -12.18 x_{6} & -0.37 x_{11}\\
 x_{10}   &  4.76076555024 & -43.83 x_{4} & + 40.32 x_{2} & +  7.76 x_{13} & +  1.56 x_{12} & + 48.60 x_{5} & -21.70 x_{1} & -70.59 x_{6} & +  3.68 x_{11}\\
 x_{8}   &  0.315789473684 & +  4.58 x_{4} & -3.26 x_{2} & -0.68 x_{13} & -0.11 x_{12} & -4.32 x_{5} & +  1.84 x_{1} & +  6.26 x_{6} & -0.26 x_{11}\\
 x_{7}   &  0.99043062201 & +  0.41 x_{4} & -0.51 x_{2} & -0.01 x_{13} & -0.06 x_{12} & +  0.46 x_{5} & -0.27 x_{1} & +  0.42 x_{6} & -0.05 x_{11}\\
 x_{3}   &  3.4976076555 & +  2.85 x_{4} & -2.63 x_{2} & -0.50 x_{13} & -0.01 x_{12} & -3.13 x_{5} & +  0.93 x_{1} & +  4.35 x_{6} & -0.26 x_{11}\\
\hline
z    &  10.0717703349 & -8.55 x_{4} & -3.20 x_{2} & +  0.07 x_{13} & +  0.43 x_{12} & -4.98 x_{5} & -4.99 x_{1} & +  0.38 x_{6} & -0.11 x_{11}\\
\end{array}\]


 $ x_{6} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  30.9299850888 & -1.86 x_{4} & -11.14 x_{2} & +  0.41 x_{13} & +  0.24 x_{12} & -1.32 x_{5} & -14.22 x_{1} & +  0.17 x_{10} & -1.00 x_{11}\\
 x_{6}   &  0.0674393384845 & -0.62 x_{4} & +  0.57 x_{2} & +  0.11 x_{13} & +  0.02 x_{12} & +  0.69 x_{5} & -0.31 x_{1} & -0.01 x_{10} & +  0.05 x_{11}\\
 x_{8}   &  0.738172698929 & +  0.69 x_{4} & +  0.31 x_{2} & +  0.00 x_{13} & +  0.03 x_{12} & -0.00 x_{5} & -0.08 x_{1} & -0.09 x_{10} & +  0.06 x_{11}\\
 x_{7}   &  1.01850345669 & +  0.15 x_{4} & -0.27 x_{2} & +  0.04 x_{13} & -0.05 x_{12} & +  0.75 x_{5} & -0.40 x_{1} & -0.01 x_{10} & -0.03 x_{11}\\
 x_{3}   &  3.79124305273 & +  0.15 x_{4} & -0.14 x_{2} & -0.02 x_{13} & +  0.08 x_{12} & -0.14 x_{5} & -0.41 x_{1} & -0.06 x_{10} & -0.04 x_{11}\\
\hline
z    &  10.0972617595 & -8.78 x_{4} & -2.98 x_{2} & +  0.11 x_{13} & +  0.44 x_{12} & -4.72 x_{5} & -5.11 x_{1} & -0.01 x_{10} & -0.09 x_{11}\\
\end{array}\]


 $ x_{12} $ enters and $ x_{7} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  35.9451476793 & -1.14 x_{4} & -12.47 x_{2} & +  0.59 x_{13} & -4.92 x_{7} & +  2.38 x_{5} & -16.17 x_{1} & +  0.14 x_{10} & -1.16 x_{11}\\
 x_{6}   &  0.535864978903 & -0.55 x_{4} & +  0.45 x_{2} & +  0.13 x_{13} & -0.46 x_{7} & +  1.03 x_{5} & -0.49 x_{1} & -0.02 x_{10} & +  0.04 x_{11}\\
 x_{8}   &  1.44725738397 & +  0.79 x_{4} & +  0.13 x_{2} & +  0.03 x_{13} & -0.70 x_{7} & +  0.52 x_{5} & -0.36 x_{1} & -0.09 x_{10} & +  0.04 x_{11}\\
 x_{12}   &  21.135021097 & +  3.08 x_{4} & -5.59 x_{2} & +  0.75 x_{13} & -20.75 x_{7} & + 15.58 x_{5} & -8.22 x_{1} & -0.12 x_{10} & -0.64 x_{11}\\
 x_{3}   &  5.52742616034 & +  0.40 x_{4} & -0.60 x_{2} & +  0.04 x_{13} & -1.70 x_{7} & +  1.14 x_{5} & -1.08 x_{1} & -0.07 x_{10} & -0.09 x_{11}\\
\hline
z    &  19.3755274262 & -7.43 x_{4} & -5.43 x_{2} & +  0.44 x_{13} & -9.11 x_{7} & +  2.12 x_{5} & -8.71 x_{1} & -0.06 x_{10} & -0.37 x_{11}\\
\end{array}\]


 $ x_{5} $ enters and Unbounded Dictionary!


 $ x_{5} $ enters and Unbounded Dictionary!
\end{document}
